Question

From the top of a cliff, the angle of depression of car on the ground is ${60}^o$. If the car is at a distance of 30 m from the cliff. Find the height of the cliff.

• A. $52m$
• B. $51m$
• C. $55m$
• D. $56m$

Answer 1

Answer: (A)

$52m$

Given that, the angle of depression of car on the ground from the top of a cliff is ${60}^0$. Also, the car is at a distance of $30m$ from the cliff.

To find out: The height of the cliff.

Based on the given information, we can draw the figure shown above.

$\therefore \angle PAC=\angle ACB={60}^0$

Now, in $\Delta ABC$,

$\tan {60}^0=\frac{AB}{BC}[\because \tan \theta =\frac{P}{B}]$

$\Rightarrow AB=30\times \tan {60}^0$

$\Rightarrow AB=30\times \sqrt{3}[\because \tan {60}^0=\sqrt{3}]$

$\Rightarrow AB=30\times 1.732$

$\therefore AB\approx 52m$

Hence, the height of the cliff is approximately $52m$.